On the sojourn time of sessions at an ATM buffer with long-range dependent input traffic

Several recent empirical studies of traffic to be carried by broadband networks have established the importance of studying queueing behaviour with traffic models having long-range dependence. We consider discrete time models for an ATM buffer fed by a class of long-range dependent arrival processes that includes the asymptotically self-similar arrival processes of the kind recently proposed by Likhanov et al. (1995). An arrival model in this class is parametrized by a session generation rate λ>0, a cell generation rate per session R>0, and and session duration random variable r which is positive integer valued with finite mean and infinite variance and has regularly varying tail, i.e. P(τ>t)~t^-αL(t) where 1<α<2 and L(·) is a slowly varying function. The service is modelled by a single parameter, the service rate s>0. The stability condition s>RλEτ is assumed to hold. We study the asymptotics of the tail of the stationary sojourn time distribution of a typical session